Question 150833: Systems of Equations and Inequalities
i) Problem: The students from algebra class go for coffee together every day at 9:00 AM. On Monday, Jordan paid $5.45 for three cartons of milk, four cups of coffee, and seven doughnuts. On Tuesday, Ryan paid $5.30 for four milks, two coffees, and eight doughnuts. On Wednesday, Zack paid $5.15 for two milks, five coffees, and six doughnuts.
(1) Set up a system of equations to model this scenario.
(2) Determine the cost of one carton milk, one coffee, and one doughnut by solving the system.
(3) If on Thursday, Taylor had to pay for five milks, two coffees and nine doughnuts, then how much did he spend?
(4) Explain the problem and the steps to solve this problem
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 3m + 4c + 7d = 5.45
4m + 2c + 8d = 5.30
2m + 5c + 6d = 5.15
-------------------------
subtract 3rd equation from 1st to get:
m - c + d = 0.30
4m + 2c + 8d = 5.30
2m + 5c + 6d = 5.15
-----------------------
subtract 4 times 1st from 2nd;
subtract 2 times 1st from 3rd:
m - c + d = 0.30
0 + 6c + 4d = 4.10
0 + 7c + 4d = 4.55
----------------------
interchange 2nd and 3rd to get:
m - c + d = 0.30
0 + 7c + 4d = 4.55
0 + 6c + 4d = 4.10
------------------------
subtract 3rd from 2nd to get:
m - c + d = 0.30
0 + c + 0 = 0.45
0 + 6c + 4d = 4.10
----------------------
At this point you can see that c = 0.45
-------------
Subtitute that into the 3rd equation to solve for "d":
6(0.45) + 4d = 4.10
2.7 + 4d = 4.10
4d = 1.40
d = 0.35
----------------
Substitute the values of c and d into the 1st equation to solve for "m":
m - 0.45 + 0.35 = 0.30
m - 0.10 = 0.30
m = 0.40
-----------------
one mild costs 40 cents
one coffee costs 45 cents
one doughnut costs 35 cents
============================
Cheers,
Stan H.
|
|
|
